Electronics > Beginners
Four questions about (Super) capacitors in series
havewattwilltravel:
I'm trying to wrap my head around capacitors in series to see if I really understand them.
1. Suppose I were to put 10 perfectly matched 1F capacitors in series and charge the series to 10V. Would each capacitor actually have the same charge/voltage, or would they vary slightly (and consistently) by position, with the outermost capacitors charged slightly more than the inner ones? (I'm thinking even if the ESR were the same for each cap, there's still a time delay as they charge that would leave them imbalanced.)
2. Suppose I charged each capacitor to exactly 1V and left them for 10 days. If the leakage current was the same for each cap, would the charge/voltage be the same, or would they again vary (consistently) by position? (Would some of the leakage current effectively charge the outer caps rather than just heating them all evenly?)
3. If that same string were partially discharged, would the resultant voltage on the outer capacitors be slightly less than those on the inner capacitors? (Because of ESR, wouldn't the outer caps be discharging into slightly lower resistance than the inner ones?)
4. Assume I were to use real capacitors and compensate for the individual differences in capacitance and leakage by putting additional capacitors and resistors in parallel with each capacitor in the string to make them equal. Would they remain balanced over time, or do the parameters for each capacitor vary individually so much over time that they'd always get out of balance?
David Hess:
The series position will have no effect except through electrostatic and magnetic coupling at very high frequencies and through mechanical layout which could result in different temperatures of operation. In practical purposes, these can be ignored except for temperature effects in high ripple current applications.
helius:
--- Quote from: havewattwilltravel on August 23, 2018, 06:26:56 pm ---1. Suppose I were to put 10 perfectly matched 1F capacitors in series and charge the series to 10V. Would each capacitor actually have the same charge/voltage, or would they vary slightly (and consistently) by position, with the outermost capacitors charged slightly more than the inner ones?
--- End quote ---
The charge on each capacitor in series is the same because charge is conserved. The total charge put onto one plate of a capacitor is equal to the charge out of the other plate, and this is transitive across all of the series capacitors. The voltage on each capacitor will be according to V = C/Q; so if they all have the same capacitance, they will all have the same voltage.
--- Quote ---(I'm thinking even if the ESR were the same for each cap, there's still a time delay as they charge that would leave them imbalanced.)
--- End quote ---
ESR doesn't matter here, and there is no time delay. Each capacitor is charged simultaneously—obviously not in a bare instant, but the current through the series string charges them at the same rate.
--- Quote ---2. Suppose I charged each capacitor to exactly 1V and left them for 10 days. If the leakage current was the same for each cap, would the charge/voltage be the same, or would they again vary (consistently) by position? (Would some of the leakage current effectively charge the outer caps rather than just heating them all evenly?)
--- End quote ---
Leakage is modeled by a parallel resistance, not a current; but you specified that the leakage currents were equal. Well, okay: if you integrate a current over a period of time, the result is a certain change in charge. This has nothing to do with capacitors.
--- Quote ---3. If that same string were partially discharged, would the resultant voltage on the outer capacitors be slightly less than those on the inner capacitors? (Because of ESR, wouldn't the outer caps be discharging into slightly lower resistance than the inner ones?)
--- End quote ---
By the same reasons as (1), they discharge equally. ESR is a series resistance, and several resistors in series are equivalent to one. Different ESR does not effect them differently, they all see the same series resistance.
--- Quote ---4. Assume I were to use real capacitors and compensate for the individual differences in capacitance and leakage by putting additional capacitors and resistors in parallel with each capacitor in the string to make them equal. Would they remain balanced over time, or do the parameters for each capacitor vary individually so much over time that they'd always get out of balance?
--- End quote ---
You didn't specify what "make them equal" means. As noted above, variations in capacitance and ESR have no effect whatsoever on the state of charge; the voltage will depend on the capacitance of each one according to the capacitor equation. The only reason to balance capacitors in series is leakage, since it acts as a parallel resistor that discharges each cap separately. If the caps have different leakage, some will discharge more than others—this can cause problems when the series is charged again, and the caps with lower leakage start from a higher state of charge, which could make them exceed their voltage specification. The way to deal with this is to place a high-value resistor in parallel with each individual capacitor, in effect overwhelming the unknown leakage with a predictable discharge.
ArthurDent:
I had bought one of the 6 supercap units on Ebay to check out and see if I could use it to power a low current (35Ma) circuit during power outages. It consisted of six 500F 2.7VDC supercaps in series for about 80F @ 16.2VDC max with equalization circuits across each cap for protection.
What I found was that 2 of the caps had high leakage so if I charged the bank up to 2.7VDC per cap and let them set, the 2 worst caps would discharge below 1 VDC quite fast. I bought 2 replacement caps from another vendor and the replacements worked better. One of the remaining original caps would discharge much more rapidly under load than the rest indicating it had less capacity (1/2?) than the rest so to get full benefit from the bank I would have to replace that cap as well. I found that to keep them charged (or ‘float’) needed about 25Ma current to compensate for the leakage.
The equalization circuit consisted of a MOSFET switch and a comparator on each cap that would place a resistor load across each individual cap if the voltage reached 2.7VDC because going above that rating could be very bad. You also have to be very careful not to short the caps because they are capable of many amps of current output. Some of the larger banks of supercaps have been used to replace car batteries and start the car which requires massive current.
So to answer your question from my experience I would say that although while the caps position in the series will not matter, that this may not work as well as you hope. I do believe that where your caps have much less capacity than mine and you probably won’t experience problems to the extent I did with mine, which were cheap Chinese caps, they may not work as well as you think they should. The smaller values around 1F are used for memory back-up in some electronics so your plan might work but you might want to do some testing like I did before you wire them into your device.
havewattwilltravel:
My intuition isn't agreeing with physics, but which one of these two is wrong? :-//
With three capacitors in series, with the leads connected end-to-end and a battery to the other ends, the resistance between the middle capacitor and the other two is (at least) twice the resistance between the end capacitors and the battery. If the battery briefly charged them, and was disconnected, why wouldn't the middle capacitor have less charge than the ends?
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